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If int(0)^(pi//2) log cos x dx =(pi)/(...

If `int_(0)^(pi//2) log cos x dx =(pi)/(2)log ((1)/(2)),` then `int_(0)^(pi//2) log sec x dx =`

A

`(pi)/2 log(1/2)`

B

`1-(pi)/2log(1/2)`

C

`1+(pi)/2log(1/2)`

D

`(pi)/2log2`

Text Solution

Verified by Experts

The correct Answer is:
D
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TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
  1. Which of the following is true?

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  2. int(0)^((pi)/2)(sinx+cosx)/(sqrt(1+sin2x))dx=

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  3. If int(0)^(pi//2) log cos x dx =(pi)/(2)log ((1)/(2)), then int(0)^(...

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  4. If int(0)^(1) tan^(-1) x dx = p , then the value of int(0)^(1) tan^(-1...

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  5. int(-pi/4)^(pi/4)(dx)/(1+cos2x) is

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  6. int(0)^((pi)/2)(cos2x)/(cosx+sinx)dx=

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  7. int(0)^((pi)/2)cos^(6)x dx=

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  8. int(-1)^(0) (dx)/(x^(2) + 2x + 2 ) is equal to

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  9. int(0)^(sqrt(2))sqrt(2-x^(2))dx=?

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  10. int(0)^(1) (dx)/(e^(x) +e^(-x)) dx is equal to

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  11. 3a int(0)^(1) ((ax-1)/(a-1))^(2) dx is equal to

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  12. int (0) ^(pi//4) sin (x- [x])d (x-[x]) is equal to

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  13. The function L(x)=int(1)^(x)(dt)/t satisfies the equation

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  14. If overset(b)underset(a)int {f(x)-3x}dx=a^(2)-b^(2), then the value of...

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  15. The value of the integral l = int(0)^(1) x(1-x)^(n) dx is

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  16. int(0)^(pi//4)(cosx-sinx)dx+int(pi//4)^(5pi//4)(sinx-cosx)dx+int(2pi)^...

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  17. Let d/(dx)F(x)=((e^(sinx))/x),x > 0. If int1^4 3/x e^s in x^3dx=F(k)-...

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  18. Suppose that F (x) is an antiderivative of f (x)=sinx/x,x>0 , then...

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  19. The value of integral int (1//pi)^(2//pi)(sin(1/x))/(x^(2))dx=

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  20. The value of the integral int(0)^((pi)/4)(sqrt(tanx))/(sinx cos x) dx ...

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